Jordan, Thomas, Kesseboehmer, Marc, Pollicott, Mark and Stratmann, Bernd O. (2009) Sets of nondifferentiability for conjugacies between expanding interval maps. In: International Conference on Dynamical Systems held in honor of Michal Misurewicz, Polish Acad Sci, Inst Math, Bedlewo, Poland, 2008. Published in: Fundamenta Mathematicae, Vol.206 pp. 161-183. ISSN 0016-2736. doi:10.4064/fm206-0-10

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Abstract

We study differentiability of topological conjugacies between expanding piecewise C1+epsilon interval maps. If these conjugacies are not C-1, then their derivative vanishes Lebesgue almost everywhere. We show that in this case the Hausdorff dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Moreover, by employing the thermodynamic formalism, we show that this Hausdorff dimension can be determined explicitly in terms of the Lyapunov spectrum. These results then give rise to a "rigidity dichotomy" for the type of conjugacies under consideration.

Item Type:	Conference Item (Speech)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Fundamenta Mathematicae
Publisher:	Polska Akademia Nauk
ISSN:	0016-2736
Official Date:	2009
Dates:	Date Event 2009 Published
Volume:	Vol.206
Number of Pages:	23
Page Range:	pp. 161-183
DOI:	10.4064/fm206-0-10
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Conference Paper Type:	Speech
Title of Event:	International Conference on Dynamical Systems held in honor of Michal Misurewicz
Type of Event:	Conference
Location of Event:	Polish Acad Sci, Inst Math, Bedlewo, Poland
Date(s) of Event:	2008

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